Question

A set of data is normally distributed with a mean of 455 and a standard deviation of 25. What percent of the data is in the interval 405–455?

a.
47.5%
c.
68.3%
b.
49.85%
d.
34.15%

Answer 1

a. 47.5%

Explanation:

1. Find the z-score for 405: 405-455/25 = -2

2. Find the z-score for 455: 455-455/25 = 0

3. Using technology or a chart, find the percentage that corresponds with the z-scores: -2 = 0.0228 or 2.28%, AND 0 = 0.5000 or 50%

4. Find the difference between the percentages by subtracting them: 50% - 2.28% = 47.72%

5. Most of the time, the answers aren't exact, so since 47.72% is closest to 47.5%, I would say that's the answer.